Models of Bihyperelliptic Curves

Abstract

We give an explicit description of the minimal regular model of bihyperelliptic curves with semistable reduction over a local field of odd residue characteristic. We do this using a generalisation of the cluster picture; a completely combinatorial object attached to a hyperelliptic curve $y^2 = f(x)$ over $K$ which contains the data of the $p$-adic distances between the roots of $f$. We add some information, resulting in a chromatic cluster picture, and show that this determines the minimal regular model of $Y$ with the action of Frobenius.